Can you clear the System Console without restarting Blender?
Below is an example add-on that adds a button to the text editor for this purpose. Clearing the console is done with the platform specific commands cls for Windows and clear for Linux and macOS. Both are executed through os.system(command)

bl_info = {
    &quot;name&quot;: &quot;Clear System Console&quot;,
    &quot;author&quot;: &quot;Robert Guetzkow&quot;,
    &quot;version&quot;: (1, 0, 0),
    &quot;blender&quot;: (2, 81, 0),
    &quot;location&quot;: &quot;Text Editor Header&quot;,
    &quot;description&quot;: &quot;Clear the system console.&quot;,
    &quot;wiki_url&quot;: &quot;&quot;,
    &quot;category&quot;: &quot;Text Editor&quot;}

import bpy
import os


class CLEARCONSOLE_OT_clear(bpy.types.Operator):
    bl_idname = &quot;clearconsole.clear&quot;
    bl_label = &quot;Clear System Console&quot;
    bl_description = &quot;This operator clears the system console.&quot;
    bl_options = {&quot;REGISTER&quot;}

    def execute(self, context):
        if os.name == &quot;nt&quot;:
            os.system(&quot;cls&quot;) 
        else:
            os.system(&quot;clear&quot;) 
        return {&quot;FINISHED&quot;}


def draw(self, context):
    self.layout.operator(CLEARCONSOLE_OT_clear.bl_idname)


classes = (CLEARCONSOLE_OT_clear,)


def register():
    for cls in classes:
        bpy.utils.register_class(cls)
        
    bpy.types.TEXT_HT_header.append(draw)


def unregister():
    bpy.types.TEXT_HT_header.remove(draw)
    
    for cls in classes:
        bpy.utils.unregister_class(cls)


if __name__ == &quot;__main__&quot;:
    register()